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Surveys in Mathematics and its Applications

ISSN1842-6298 (electronic), 1843-7265 (print) Volume5₍₂₀₁₀₎_{, 285 – 295}

A CLASS OF ANALYTIC FUNCTIONS BASED ON

CONVOLUTION

K.G. Subramanian, T.V. Sudharsan, R. Thirumalaisamy and H. Silverman

Abstract. We introduce a classT Sg

p(α) of analytic functions with negative coefficients defined

by convolution with a fixed analytic functiong(z) =z+P∞ n=2bnz

n_,_b

n>0,|z|<1. We obtain the

coefficient inequality, coefficient estimate, distortion theorem, a convolution result, extreme points and integral representation for functions in the classT Sg

p(α). Full text

References

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2010 Mathematics Subject Classification: 30C45; 30C50.

Keywords: Analytic functions; Starlike functions; Convolution.

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2 _{K.G. Subramanian, T.V. Sudharsan, R. Thirumalaisamy and H. Silverman}

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Func-tions with positive coefficients defined using convolution, J. Ineq. Pure and Appl.

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K.G. Subramanian T.V. Sudharsan

School of Mathematical sciences, Department of Mathematics, Universiti Sains Malaysia, SIVET College,

11800 Penang, Malaysia. Chennai 601 302 India.

e-mail: [email protected] e-mail: [email protected]

R. Thirumalaisamy H. Silverman

Department of Mathematics, Department of Mathematics, Government Arts College, College of Charleston, Chennai 600 035 India. Charleston SC 29424, USA. e-mail: [email protected] e-mail: [email protected]

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